with \(\omega _k = \sqrt{\vec{k}^2 + m^2}\) , denoting the Jordan–Pauli function [1]}, also called
Hadamard function [2]}. It has the contour integral representation
\(\Delta (x) &=& \int _{C_0} \frac{d^D k}{(2\pi )^D} \frac{e^{ik.x}}{k^2 - m^2}= \Delta _+(x) + \Delta _-(x) = \Delta _{\rm ret}(x) - \Delta _{\rm adv}(x),\) 
